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QurvE: user-friendly software for the analysis of biological growth and fluorescence data

Nature Protocols volume 18, pages 2401–2403 (2023)Cite this article

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The study of growth (of cells, organisms or populations) is inherent to all biological disciplines. The fundamental properties of a biological system or the physiological effects of an experimental setup (e.g., the presence of a toxic compound, substrate availability or implantation of a synthetic pathway) can be investigated by tracking growth over time1,2,3. In applied biosciences, isothermal growth, where the temperature remains constant, is the most commonly used experimental setup. This approach simplifies data analysis and model fitting by eliminating the influence of varying temperature on growth dynamics4. Laboratory automation is increasing the throughput of such data5, but analysis remains tedious and time-consuming6. Most studies report physiological and kinetic parameters without a wide consensus on how to derive them from experimental data. Furthermore, existing analytical tools often require expert knowledge or programming skills.

The software is designed to streamline the process of obtaining quantitative physiology parameters from raw data (e.g., optical density measurements in the case of microbial cultivations). With high-throughput cultivation devices becoming increasingly accessible, multiple growth curves (up to several hundred) can be recorded simultaneously — rendering their analysis tedious and time-consuming. Moreover, some integrated devices (e.g., microtiter plate readers) can also be used to track changes in fluorescence over time. Fluorescent tags added to proteins and transcriptional reporter studies have become commonplace techniques to study the structure of biochemical networks, differences between specific and generic responses based on growth rates or the role of key effectors in controlling gene expression. To analyse these types of data and to obtain biologically relevant parameters, researchers fit mathematical models to the datasets and determine the optimal parameters. To fulfil this purpose, QurvE provides a wide range of fitting options and visualization capabilities. QurvE accepts raw data produced by a variety of proprietary software tools for different growth- or fluorescence-measuring devices, e.g., plate readers and micro-bioreactors, which can be directly parsed into a compatible format. Alternatively, any type of experimental data can be loaded after formatting into a simple table format (Fig. 1b). Then, data fitting and determination of biological parameters are performed using three methods:

  1. 1.

    Fitting of isothermal growth models, including automatic model selection for each sample based on the Akaike information criterion (AIC) and parameter inference. Five commonly used models for net growth are supported: logistic growth, Richards, Gompertz, extended Gompertz, and Huang and Baranyi7,8,9 (Fig. 1c).

  2. 2.

    Linear regression on the (log-)linear part of a curve with the Theil–Sen estimator as a more robust alternative to the traditional least-squares method10 (Fig. 1d), which also allows for parameter calculation of a secondary growth phase in bilinear curves.

  3. 3.

    Smoothing splines, which model a wide range of curves without a priori assumptions about their shape7 (Fig. 1e), are robust to outliers and account for nonlinearity while preserving the underlying signal. QurvE incorporates bootstrapping for spline fitting, enhancing the reliability of curve fits by estimating uncertainty, validating the model and identifying potential outliers.

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Fig. 1: QurvE enables robust, high-throughput analysis of growth and fluorescence data.

Data availability

Input data used as examples in this article are embedded in the R package as part of the function help documentation and the accompanying manuals. Further example files and data therein can be found at https://github.com/NicWir/QurvE/tree/master/examples.

Code availability

QurvE is published under the GNU General Public License version 3 and is available as an R package on the Comprehensive R Archive Network (CRAN). The source code, along with the most recent development version, can be found at https://github.com/NicWir/QurvE. Documentation, tutorials, troubleshooting guidelines, and the Shiny app, which can be installed as standalone software, can be accessed and downloaded from https://nicwir.github.io/QurvE. Additionally, the Shiny app is available as a web-based application accessible through any browser at https://www.qurveanalysis.com/.

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  3. Wirth, N. T. et al. Metab. Eng. 74, 83–97 (2022).

  4. Neidhardt, F. C. J. Bacteriol. 181, 7405–7408 (1999).

  5. Gurdo, N., Volke, D. C. & Nikel, P. I. Trends Biotechnol. 40, 1148–1159 (2022).

  6. Swain, P. S. et al. Nat. Commun. 7, 13766 (2016).

  7. Kahm, M., Hasenbrink, G., Lichtenberg-Fraté, H., Ludwig, J. & Kschischo, M. J. Stat. Software 33, 1–21 (2010).

  8. Huang, L. Food Microbiol. 28, 770–776 (2011).

  9. Baranyi, J. & Roberts, T. A. Int. J. Food Microbiol. 26, 199–218 (1995).

  10. Theil, H. in Henri Theil’s Contributions to Economics and Econometrics: Econometric Theory and Methodology (eds Raj, B. & Koerts, J.) 345–381 (Springer, 1992).

  11. Ritz, C., Baty, F., Streibig, J. C. & Gerhard, D. PLoS ONE 10, e0146021 (2015).

  12. Meyer, A. J., Segall-Shapiro, T. H., Glassey, E., Zhang, J. & Voigt, C. A. Nat. Chem. Biol. 15, 196–204 (2019).

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Acknowledgements

We are indebted to the growing community of QurvE users for their feedback and suggestions. This study was supported by grants from the Novo Nordisk Foundation (NNF20CC0035580, LiFe (NNF18OC0034818) and TARGET (NNF21OC0067996)), the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 814418 (SinFonia) and the Cystic Fibrosis Trust, Strategic Research Centre Award–2019–SRC017 to P.I.N.

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  1. The Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, Kongens Lyngby, Denmark

    Nicolas T. Wirth, Jonathan Funk, Stefano Donati & Pablo I. Nikel

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  1. Nicolas T. Wirth
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  2. Jonathan Funk
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Contributions

N.T.W. conceptualized and designed the project and is the main developer and maintainer of the QurvE package; J.F. contributed to writing the code for the Shiny app; S.D. contributed to the design, testing and documentation; N.T.W. and P.I.N wrote the paper; P.I.N. supervised the whole project and secured funding.

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Correspondence to Pablo I. Nikel.

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The authors declare no competing interests.

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Nature Protocols thanks Michael Kuhn and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Wirth, N.T., Funk, J., Donati, S. et al. QurvE: user-friendly software for the analysis of biological growth and fluorescence data. Nat Protoc 18, 2401–2403 (2023). https://doi.org/10.1038/s41596-023-00850-7

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